Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×C32×C3⋊D3 |
| Fitting, socle | C22×C34 ⋊ C2 |
| derived | C32 ⋊ C23×C32 |
| Sylow | C34 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C32 | |
1016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#3722, C3×#88803, C3×#88814, … |
| maximal normal subgroup of | C32×#3722, C3×#88803, C3×#88814, … |
| maximal quotient of | C2×C32×#634, C2×C32×C4×C3⋊D3, C2×C32×C4⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 754);